ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   172.   75.5 Green     
 2     2   175.   84.9 Brown     
 3     3   162.   85.1 Blue      
 4     4   169.   62.1 Green     
 5     5   168.   76.2 Green     
 6     6   171.   77.2 Green     
 7     7   168.   60.2 Blue      
 8     8   182.   95.6 Blue      
 9     9   176.   67.6 Blue      
10    10   168.   79.9 Brown     
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1]  0.4377817924 -1.6704052694 -0.6900665150 -0.9569637184 -1.2620415298
   [6]  0.7611878818 -0.5188505036  0.5337994416 -0.6939479715  1.0864202205
  [11] -0.1908661480  1.4129415495 -1.3653456448 -1.7623498997  0.6411850318
  [16]  0.0950239333  0.9812742359  0.4618999394  0.0001753786 -2.6952799846
  [21]  0.5096343194 -0.0743555009  0.0102834064  3.2387318075 -0.9475898826
  [26]  0.5801454353 -0.0932459528  1.1562303591  0.3857142021  0.6139360572
  [31] -0.5507360607 -0.1031133328  0.3277378291  0.9481982794  1.4505379825
  [36]  0.6364883267 -1.1958911792  1.0562060767 -0.7407629476 -0.6794582597
  [41]  0.2694981058 -0.5376435903  0.2634651119  1.0309643883 -0.7106894031
  [46] -1.1249916355 -1.6844389378  0.5184033201 -0.8126450548 -1.4547705261
  [51] -0.2036015548 -0.8307122859  0.2860469523  0.5382817627  1.2190311753
  [56] -2.8188388547 -2.3437365571 -1.7974918457  2.4580413820 -0.2178647254
  [61]  1.0287974487 -1.9130631572 -0.7306430119 -0.7233886532  1.6994700624
  [66] -0.2152500085 -1.6553482257  0.1892765710  1.0346872664  0.2385212821
  [71]  0.1758293656  0.1423945996  0.5857730364  0.3443242357 -0.6802308292
  [76]  1.1453791835  0.1061917378 -1.4643610790  0.4640947037  0.8387177426
  [81]  0.7124942957 -0.0702101378 -0.0494196219  0.2163902143 -0.9980659992
  [86] -0.8313432623 -1.0011343416  0.3882905485 -0.1251197041  0.0121228249
  [91]  0.2639782608  1.2894277476  0.6249621295 -0.1811783536  0.9655923026
  [96] -0.0502037998 -1.0103921201 -0.6459277854 -0.6111715961  0.1925653186
 [101]  1.5974581296  0.3918901836 -1.1978129429  0.4590805862 -0.6518279675
 [106]  1.0294760542 -1.1194480822  0.3104921736  0.9531991733 -0.2490029942
 [111]  0.7702749269  0.5951021935 -0.5784276779  0.1118814805 -1.8594653117
 [116] -0.0219226320  0.1006978054 -0.2090532690  1.4893534908  0.6307221328
 [121] -0.3663095660 -0.8377867340 -0.6935060466  0.5827085391  0.1870165282
 [126] -0.3927973296 -0.0055678166 -0.5045999780  1.3527088588  1.5264456460
 [131]  0.0133863917 -0.1472726095 -1.6537079580  1.6176281675  0.4722810303
 [136] -0.4594289755  0.9633629700  1.0087032222  1.3104468762 -0.5544084205
 [141] -0.2359628526 -1.3847596342 -0.3714404415 -1.7216070193 -0.6507076962
 [146]  0.1867419845  0.6038133054  0.3785736666  0.5831373141  0.8261147419
 [151]  1.1558291913 -1.1513916895  0.2361639300 -0.3816693812 -0.0647652131
 [156]  1.1019485744  2.3857781611 -0.9205922512 -1.1340584173 -0.3232431717
 [161] -0.3270927254 -0.0169595427 -0.3217115920 -2.0803991750 -0.3798374607
 [166] -0.4497669075  0.2026694426  2.3106779516 -0.1399851719 -0.8464833358
 [171] -0.2652598551  0.1965875296  0.2780190653 -1.0806198880  0.1357021350
 [176] -0.8354104168  0.4457190516  0.7674491478 -0.0282492025  0.0219652902
 [181]  0.3503742159 -1.3901331752  0.5620852847 -1.9093213388  0.6378530655
 [186] -0.1046932153  0.5791171755  1.9105976138  0.6469437479  0.0020232921
 [191] -0.2950666522 -1.0436819765 -1.1427285063  0.6454749142  1.9504216905
 [196]  0.7501400114 -0.8698448148  0.1190694013  2.0330089717  2.2346609909
 [201]  0.0881176715  1.1415082272  0.4601289764  0.6486655904  0.9059309256
 [206]  0.4037628523 -0.7423678935 -0.3609420974 -1.4690301251  1.1360952764
 [211]  1.8436670289  2.6324729891  0.6583601544 -0.8510834971 -0.0448759041
 [216]  0.7151301909 -0.3173581291 -0.5003050123  1.1253171357 -0.1946818899
 [221]  1.6013275717 -2.2559680437  0.6427539601  0.5060306939  0.2824283328
 [226]  1.6762971964  0.2076595620 -0.7840463681  1.7782582217 -0.7997667549
 [231]  0.3273365916 -1.1295503517  0.6356289061 -0.3197109524 -0.2446132114
 [236] -1.3134569952  0.0491619370  0.4866842713  0.2314383264  0.6138944204
 [241]  1.2212482994  1.1154893342 -0.2655222817 -0.1787600308 -0.3626296520
 [246]  1.3766461339 -0.1268899852 -0.2229546246  0.6381120810  1.6567101720
 [251]  0.6702825496  1.0406464920  1.1735800223  0.0723163523  0.7719816089
 [256]  0.9233579533 -0.0854578832 -0.5103797479  1.2855217542  1.5400517384
 [261] -2.0970309662 -0.5098704346  0.1769637095  0.2177920752  1.4503859758
 [266] -0.3749944305 -0.6031338961  0.0405415082  0.7056668191  0.4008189418
 [271] -0.3308641397 -0.1952740171  0.2066852033  1.0586802775 -0.8729452566
 [276]  0.8014873401  0.5112593413  0.5805187553 -0.0777333943 -0.3494920156
 [281] -1.3522268586 -0.7428099165 -1.0865262539  0.3052794927  0.1394059988
 [286] -1.7903544322  2.0462046873 -0.0960542459 -0.7999755261  0.8166212669
 [291] -0.9366169082 -0.3803460417 -0.7594981247 -1.1457293103 -1.7641296058
 [296]  0.2769663630  0.0350679233  0.3785786718 -0.7558513630 -0.2546043610
 [301] -0.0627531875 -1.4667479689 -1.5067257958  0.4446588878  0.0245924315
 [306] -0.3501265160 -0.9930873053  0.2226004242 -1.0351508134 -0.9681101373
 [311]  0.2839541303 -1.1614198756 -0.5398158764 -3.0916977618 -0.0817827419
 [316]  0.0228584995  1.0347753185  1.0952621072 -3.2015117664  1.3095231977
 [321]  1.9885886087 -0.5344900807 -2.0102048353 -0.1345289814  0.4961790248
 [326] -1.7089660007 -0.0353072756  0.4200959981  1.8491985286  2.0096122268
 [331]  1.0045676845 -2.0913576004 -1.2105605584 -1.1356933202 -1.9666500386
 [336] -0.1301280093  0.0237084891  0.3296293150 -0.0502864951  1.6810405452
 [341] -0.9394540942  0.9027337754  0.3369244597 -0.7562559146 -0.1489020533
 [346] -0.7297162628  0.7714667671  0.6091036135 -2.3034064964  0.5751383203
 [351]  1.2399552692  0.6626685614 -0.4261729700 -0.8000370632  0.8923727218
 [356]  0.4411538891  1.3965326488 -0.3075616830 -0.1062134248 -0.3233927911
 [361] -0.1052354140 -0.6727885704 -1.8794672692  0.2580534903 -0.9034075452
 [366] -0.0559718432 -0.4211608010 -1.4094170190  1.0683168364 -0.7856473097
 [371]  0.5912431851  0.2744796526 -0.5365526994  0.4190994930 -0.7453280366
 [376] -0.2671162772 -1.2899758470 -1.6424491591 -0.3510788601 -0.0177516606
 [381] -0.2015402433  1.1819629804  0.7375987300 -1.0815411119 -1.1347852756
 [386]  0.6189621889  0.8879006916 -0.0973985439 -0.3079310215 -1.0214003294
 [391] -0.8230290072 -0.0366665291 -0.3657274226  0.3465139792  0.8546722501
 [396] -0.3916370156  0.1933486539  1.7541348568  0.4582645098  0.3558727668
 [401]  1.8112133096  0.6980352079 -0.2481499852  0.5193413263  0.3424129225
 [406]  1.2223515878 -1.4792238454 -0.0784797291  1.1060051734  1.5534783961
 [411]  0.0636263632 -1.4202019124  0.0137280764 -0.1518172231 -0.2358013936
 [416]  0.4667721831 -0.4542158565  0.4600609263 -1.0779824426  0.6013657868
 [421]  1.4818302238 -1.2419196811 -1.2383340955  2.2227003483  1.1725946491
 [426] -1.2203222465 -2.0907076009 -0.0355265401 -0.2749030592  1.4317232861
 [431] -1.0653914574 -2.2827992062  0.3808628359  1.2969386285 -0.6998135626
 [436]  1.0741873119 -1.4110961320  1.6840458272  1.9512494441 -0.0901318141
 [441]  0.8113285067  1.5375617376 -0.6593251442  0.4363864603 -0.6745731117
 [446] -0.8708651670 -0.8972948460  0.7855047514 -0.7740178450 -1.3039540750
 [451]  2.2574709987  0.7353116828  1.4008072356  0.1132641297  0.1321689036
 [456]  1.3106119244  0.8612700753 -0.8931086073  0.1508416830  0.2936833721
 [461]  0.7264594427 -0.1724750271  0.6368908734 -0.1844902930 -0.5058586785
 [466]  1.3147091910 -2.1819266922 -3.3590802447  0.7255277800  2.9401149233
 [471] -0.8113612911 -0.5410662201 -1.2716609251  0.4398038364  0.9539117625
 [476]  0.9973894944  0.4111744975  0.0960345959  0.4146581993  0.3298755843
 [481] -1.0029014850 -0.9268481733  1.4408414652 -0.4887013498 -0.7805044030
 [486]  1.4863825107 -1.0838337674 -1.7191943239  0.9684654907 -0.1082844144
 [491] -0.7071617447  0.8384738512 -0.0043841507 -0.9350938509  0.1572445632
 [496] -1.8969063426  0.0510324477 -0.9165977719 -1.3436123569  1.5323741957
 [501] -0.5192574275 -0.8870582470  0.2828251492  1.1743277318  1.4101217942
 [506]  1.4383378286 -1.2216246770  0.0654538254  1.4040171762 -0.0590153279
 [511] -0.1066438160 -0.7817686509  0.7996564945  0.1205220969  0.4636629155
 [516] -1.4261939669  0.6892189216 -0.5175874055 -0.8881327991 -0.9968089670
 [521]  0.9318398308 -0.8993370780 -0.9223594374 -0.4902222817  0.0640990056
 [526]  0.8922762792  0.1755879186 -1.1994314072  0.9626621080 -0.4866057217
 [531] -0.4450228900  0.4448119936 -2.0742407453  0.6071141131 -0.5704712193
 [536]  0.6433588283  0.4632748763  0.1400348564 -1.2087902327  1.5395436781
 [541]  1.2568422570  0.5783319450 -0.1700469148  1.0997897921 -0.4644735806
 [546] -0.0187516613 -0.6716226124 -0.0726523207 -2.1798413452  1.2503735078
 [551]  0.4215210782  0.0997123380  0.5634176134  0.2335818856  0.6024558728
 [556] -0.8306277478 -0.0548319509 -0.9141321679  0.3645033148 -0.4780601298
 [561]  0.6025728003 -0.8002096799 -0.2285446027  1.8070790208 -0.2818654282
 [566] -1.0803419409 -1.2420501043  2.2808353845  0.9610673531 -0.1041700687
 [571] -0.9002341154  2.7199791732 -0.5001982797  0.4963511334  1.2050024714
 [576] -0.0852274907 -0.6488321709  0.9658335582 -0.9512714468 -0.0779489272
 [581]  0.8707934012  0.7023820131 -0.9226969022  1.0006907340  2.2714997013
 [586] -0.1163245606  0.3145725402 -0.2724265340 -1.2653120037 -0.4016930873
 [591] -0.5484509680  1.3500603728 -2.3799052272  0.3361321577 -0.0194716149
 [596]  0.9943994286 -1.0969027835 -0.2358882475 -0.6043395561 -0.6706297808
 [601] -0.1091317747  0.1040444682  2.2540069776 -0.2447701874 -0.9182271946
 [606] -0.9806333091 -0.1444086165 -1.4900305395  0.3337772285  0.3799086995
 [611] -0.1886839621  0.6759912159  0.9450464285 -0.1003051001  1.0894726734
 [616] -1.4540719144  0.7968990839  0.4677854530 -0.5319130010 -0.2954426658
 [621] -1.4670323683  0.0929612242 -0.2892785945 -1.3039580500  0.2578797824
 [626]  0.1877937004 -0.7109672687 -1.7238687787  0.0637580122  0.0078279385
 [631]  1.2626600237  1.5858019222 -1.8572478590 -0.0746139318 -0.3511058425
 [636] -0.4259205365 -0.0116530157 -0.1176010020 -0.3002452029 -0.7665346198
 [641] -0.7288375231 -1.1637408158  0.3866038269 -0.0215616200 -0.1510732387
 [646] -0.5968256769  1.4983117973  0.6364787187 -0.3578709995  0.5314970309
 [651] -1.6106758701 -2.0864830626 -0.1868125318 -1.3321938903  0.0660385148
 [656]  2.4496687462  0.0194513250  0.4269742231 -1.4770325821  0.5065237129
 [661]  0.3270339034  0.0266257201  0.6199113391 -0.1542684159  0.2931469875
 [666] -0.2246957738  0.7252099775 -0.7696357708 -1.1629074478  0.1551116032
 [671] -0.7771080690 -0.6522268234  1.0217452250 -0.3187490197 -0.0727935763
 [676]  0.4049614322 -0.9196850756  0.4703590426 -0.4121499850 -1.0945249320
 [681]  0.3073348131 -1.7496764364  0.2818709409  0.4485241323  0.3711783224
 [686]  0.3366623919  0.9194047886 -0.9597198573  0.3652991767  0.7193470893
 [691]  1.4013789413  0.1189455934  2.7803347733 -0.1104263065 -1.4965414060
 [696] -1.0298488935 -1.1315843163 -1.7966228689 -0.3693436424 -0.6383558127
 [701]  0.5061770420 -0.2521991089 -1.1007277781  0.3553693498  1.7679354104
 [706]  0.0469333451  0.5794494795 -0.5534633640 -0.8571344798 -0.5632764086
 [711] -2.1586838805 -0.4705317828  0.3167405953  1.0214362159 -0.6581615448
 [716] -0.0969118571  2.1356314588  1.6028436056 -0.4576461160  0.2246994797
 [721] -0.5942320229  0.2886213414  2.0113018884  0.2239118898 -1.3516003267
 [726]  0.7093329526  0.0608708882 -0.6645316909 -0.4165485678  2.6920874240
 [731]  0.6372248066  1.4073234950 -0.7669017308  0.4415232253  1.2829321668
 [736]  1.3536614642 -1.5558996448 -0.2658687860 -1.6866760878  2.1480236117
 [741]  0.8335583421 -1.6167655480  0.1912597794 -0.1155688874 -1.1604919110
 [746] -1.2656026372 -0.4227090174  0.3906646761  2.1698118680  0.3897033269
 [751] -0.4772079105  0.2693652453  0.4086308025 -0.8763387377 -0.1595770442
 [756] -0.3205580670  2.0318222719 -0.4035967013 -1.0792040211  1.0226872784
 [761] -1.1813566978  0.0696288092 -0.5237176768  0.2417325427  0.0060386943
 [766] -0.6970441561  0.5607491315 -0.5059039223  0.2787981026  0.6565969497
 [771]  0.3205594650 -1.5727631419  2.2048105255  0.2571296899  1.6715366623
 [776]  0.2401777429  0.1858709220 -0.4436487816  0.1195543357  1.2451132058
 [781]  0.1635027378 -0.1811544186  1.5662091185 -1.7002301591 -0.0323398995
 [786]  0.3760716161 -3.0155881136  0.5756796868  0.9752139770 -2.6028891445
 [791]  0.0212895816  1.5252627045 -1.4764255777 -0.3801207244  0.5919189163
 [796] -0.2479617935 -2.5589713900 -1.1585621149 -0.0479842414  1.5874037192
 [801]  1.5261698375 -1.4958572059 -1.6780076396 -0.6780083405 -0.3112629800
 [806] -0.6251742848 -0.4589153707 -1.9985961883  1.4277028214 -0.3863453466
 [811] -0.5050499739  0.7473184589  0.6495289023  0.5120865514 -1.1965981926
 [816]  1.3707543326  0.4624353384 -0.6982100102 -0.2327510422 -0.5335503256
 [821] -0.7921988270 -0.4337174378  2.0258102856 -0.9978882625 -0.0969984987
 [826]  0.3878407266 -1.3385252795  0.7829519402 -0.2830852501  0.9630588802
 [831] -0.3995615107  0.5525977000 -1.7578688235  1.4180027844  0.6090379400
 [836]  0.2024494354 -1.5830075424 -0.8305983775  1.1984437603 -0.4795766736
 [841]  0.4916452557  0.0036286322  1.0439492126  0.3537672621  0.4193299317
 [846] -1.4238127799  0.3584184816 -0.2191407141 -0.2119574074 -0.2588354119
 [851] -0.1264828828  0.3306313085 -2.3472591747 -1.5737192000 -0.1790498057
 [856] -0.2077181974 -0.1521597344  1.8327650978 -0.1166078344 -0.7689017399
 [861] -0.2481994323 -0.7455412920 -0.4847823666  0.4432423222  0.6741441537
 [866]  0.1479927019  0.1007757805  1.6757800885  0.6454915381  0.6754624877
 [871]  1.6164755562  0.3831561086  0.1147968580  0.4361189972 -0.3133286363
 [876]  1.5276009166  0.3663144040 -0.8845497136 -0.1427166219 -0.0246612051
 [881]  0.9416910646 -0.3243440174 -0.2327407394 -0.8752247341  0.7031098303
 [886] -0.7155855834 -1.0144838165  1.8909174813  1.3458618663 -0.6464846306
 [891]  0.5296577010 -0.1831839193 -1.6032838040 -1.5972702355 -0.1483749517
 [896]  0.4151423848 -0.9326585750 -0.1876333694 -1.3021705890 -0.0823379163
 [901]  0.9142185125 -0.5972273237  0.2905658186 -0.8662223260 -0.8539289566
 [906] -0.9704449094  0.5019112872 -0.1453573596  0.3300912386 -0.9723942116
 [911] -1.6352686068  0.8607158082  1.4560629913 -0.4652452925  0.5503334957
 [916] -1.0236572177 -0.6197437693 -0.1968307125 -0.5521320101 -1.3663408144
 [921]  1.7941070120 -0.1239255128 -0.0033397406  0.9701906726  0.7766848049
 [926]  0.6064624886 -1.2869574682  0.4018196208  1.5328793088 -0.9841218509
 [931]  1.2017705618 -0.7367818777 -0.6595813599 -0.4696241499  1.5855137516
 [936] -0.8693829646 -0.9811608346 -0.2288444847  0.3173490371 -0.0592727957
 [941]  1.5550075849  0.1314021160 -1.0790771523 -1.0566474346 -0.7122311783
 [946] -1.3329784176 -1.1756911610  1.2491986840  1.8368927343 -0.5011747684
 [951]  0.0278983114  0.9496419349 -0.9480089912  0.0129110236  0.5879310057
 [956]  0.3460740684  0.1768638053 -0.4551255749 -1.2612844117  1.2931526215
 [961] -0.3943601071 -0.4688820194 -0.1154121942  0.4081637435  2.4860230437
 [966] -2.0368718162  0.7663326764  0.5360025029  0.0406132643  0.9702946431
 [971] -0.3159642291 -0.5043599495  0.4603794706  0.3996212876 -0.3521773123
 [976] -0.3519251252 -0.8508501423  0.8091356301 -0.9191044081 -1.6790224430
 [981]  0.2469016816  0.4841698671 -1.7141089504  0.8674563213  1.5239330152
 [986]  1.0026213644  0.0824857622 -0.7941718215 -1.0901429816 -0.9340656014
 [991]  0.1750716535 -0.8972599202 -0.9534241195 -0.8327137033 -0.6168292191
 [996] -2.6482941875 -0.0827203511  0.4780653477 -1.0186108666  0.9355235775

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0
  [38] 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1
  [75] 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0
 [112] 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1
 [149] 0 1 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1
 [186] 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0
 [223] 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0
 [260] 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1
 [297] 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1
 [334] 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1
 [371] 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1
 [408] 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1
 [445] 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1
 [482] 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1
 [519] 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0
 [556] 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0
 [593] 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1
 [630] 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1
 [667] 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0
 [704] 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1
 [741] 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 1
 [778] 1 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0
 [815] 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0
 [852] 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1
 [889] 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0
 [926] 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0
 [963] 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0
[1000] 1

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   172.   75.5 Green      A    
 2     2   175.   84.9 Brown      A    
 3     3   162.   85.1 Blue       B    
 4     4   169.   62.1 Green      A    
 5     5   168.   76.2 Green      A    
 6     6   171.   77.2 Green      B    
 7     7   168.   60.2 Blue       B    
 8     8   182.   95.6 Blue       A    
 9     9   176.   67.6 Blue       B    
10    10   168.   79.9 Brown      B    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups